I DO Then YOU DO

After a quick tour of the tools,

I'LL DO these ...

- Linear pair is supplementary

- Distance from angle bisector

- Construct a square

- Angle inscribed in a semicircle

YOU DO these ...

- Triangle Sum is 180 Degrees

- Pythagorean Theorem

- Construct a hexagon

- Construct a dynamic kite in a circle

Step by step ...

- Illustrating that a linear pair is supplementary:

- In the Display menu, select Preferences; set the Angle unit to Degrees; turn on Autoshow label for points.
- Use the segment tool to construct segment AB.
- Use the point tool to place a point C on segment AB.
- Use the ray tool to construct a ray CD from point C.
- Shift-select angle ACD; from the Measure menu select Angle.
- Shift-select angle BCD; Measure >> Angle.
- Marguee the two angle measurements.
- Under the Measure menu select Calculate...
- On the calculator, under the Values menu, you will see the angle measures that had been highlighted; select "∠ ACD", then select the "+" button on the calculator, then Values >> ∠ DCB; select OK. The sum will appear.
- As you grab-and-drag point D, the individual angle measures change but the sum remains 180 degrees.

- Illustrating that the distance from a point on an angle bisector to either side of the angle is the same.

Use the ray tool to construct an ∠ CAB.

- Shift-select, in order, points C-A-B (or B-A-C); Construct >> Angle Bisector.
- Place point D on the bisector.
- Shift-select point D and ray AB; Construct Perpendicular Line.
- Create the point of intersection of the perpendicular and the side by either bringing the select arrow close to the intersection and clicking, or by shift-selecting the ray and the perpendicular and using Construct >> Point At Intersection.
- Select the perpendicular; Display >> Hide. Note that the point of intersection remains visible on the side of the angle. Construct the segment from this point on the side to D on the angle bisector. Measure the length of the segment.
- Repeat this process for the segment joining point D to the other side of the angle. Slide D along the bisector and note what happens.
- What type of quadrilateral is AEDF? How could you prove it?

- Constructing a square by using transformations.

- Constructing a square using a reflection.

- Construct a vertical segment AB.
- Construct a circle with center A and radius AB.
- Construct the perpendicular to segment AB passing through point B.
- Construct C as one of the points of intersection of the perpendicular and the circle. Hide the perpendicular and the circle. Use the segment tool to construct triangle ABC.
- Select segment CA; Transform >> Mark Mirror (you'll see the select sqaure flas as bullseyes).
- Use Edit >> Select All, or drag a marquee to select all segments and points; Transform >> Reflect to create the square.
- Measure the lengths of segments AB and AC. Calculate the ratio of AC/AB. What is this value?

- Constructing a square using rotations.

- Construct a vertical segment AB.
- Double-click on point A so that it flashes as a bullseye. This shows it was marked as the center of a rotation. You can also select it and use Transform >> Mark Center.
- Select all. Transform >> Rotate. A dialog box comes up that allows you to specify the angle of rotation. Use 90 °.
- Construct segment BB'. Select this segment and Construct >> Point at Midpoint.
- Mark the midpoint as the center. Select all, Tranform >> Rotate by 180 °.

- Showing that any angle inscibed in a semicircle is a right angle.

- Let Circle (A, AB) specify the circle with center point A and radius AB. Construct circle (A, AB).
- Construct ray BA. Identify the point of intersection of the ray and the circle. Hide the ray, and construct the segment. This will create the diameter.
- Construct a random point on the circle. Connect that point to the endpoints of the diameter.
- Measure the angle whose vertex is the random point on the circle.
- Just for fun, shift-select the point and the circle; Display >> Animate slowly.

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